The value of $$\sum_{k = 1}^{13} \frac{1}{\sin\left(\frac{\pi}{4} + \frac{(k - 1)\pi}{6}\right)\sin\left(\frac{\pi}{4} + \frac{k \pi}{6}\right)}$$ is equal to

A

$$3 - \sqrt{3}$$

B

$$2(3 - \sqrt{3})$$

C

$$2(\sqrt{3} - 1)$$

D

$$2(2 + \sqrt{3})$$